Thermoelectric properties of anisotropic semiconductors

General effective transport coefficients and the thermoelectric figure of merit ZT for anisotropic systems are derived. Sizable induced transverse fields on surfaces perpendicular to the current flow are shown to reduce the effective transport coefficients. A microscopic electronic model relevant for multivalleyed materials with parabolic bands is considered in detail. Within the effective mass and relaxation-time approximations but neglecting the lattice thermal conductivity kappa(l), the thermopower and Lorenz number are shown to be independent of the tensorial structure of the transport coefficients and are therefore isotropic. ZT is also isotropic for vanishing lattice thermal conductivity kappa(l). A similar result holds in lower dimensions. For nonvanishing but sufficiently isotropic kappa(l), ZT is ordinarily maximal along the direction of highest electrical conductivity a. More general numerical calculations suggest that maximal ZT occurs along the principal direction with the largest sigma/kappa(l). An explicit bound on ZT is derived. Consideration of the Esaki-Tsu model shows that nonparabolic dispersion in superlattices has little effect on the thermopower at the carrier concentrations which maximize ZT. However, strong anisotropies develop when the chemical potential exceeds the miniband width.